Stress field analysis method and device and computer equipment

Abstract

The invention relates to a stress field analysis method and device and computer equipment. The method comprises the following steps: determining a first coordinate representation of a crack in a first plane according to an orthotropic parameter of a tunnel surrounding rock and a first geometric parameter of the crack of the tunnel surrounding rock; the first plane is a plane containing cracks in the plane where the tunnel surrounding rock is located, and stress borne by the cracks in the first plane is anisotropic; mapping the crack from the first plane to a second plane according to the orthotropic parameter and the first coordinate representation to obtain a second coordinate representation of the crack in the second plane; the stress borne by the crack on the second plane is isotropic; according to the second coordinate representation, the crack is converted to the unit circle from the second plane, and a third coordinate representation of the crack on the unit circle is obtained; and according to the third coordinate representation and a mapping relation between the first plane and the second plane, determining a target stress and a stress intensity factor borne by the crack in the first plane. By adopting the method, the stress field can be quickly analyzed.

Description

Technical Field

[0001] This application relates to the field of stress field technology, and in particular to a stress field analysis method, apparatus and computer equipment. Background Technology

[0002] In railway tunnels, slope engineering, and shale gas extraction, rock masses (such as shale, slate, and interbedded sandstone) sometimes exhibit quasi-orthogonal characteristics (equal eigenvalues) and contain internal joints and fissures in the form of flexural cracks. Under in-situ stress, the initiation and propagation of flexural cracks can lead to engineering instability or disasters. On the other hand, straight cracks may experience crack propagation path deflection under combined loading. Therefore, accurately analyzing the stress field and stress intensity factor of flexural cracks in orthogonal materials is of significant practical importance not only for tunnel and slope safety assessment and stability analysis.

[0003] Currently, existing technologies have studied the stress field of isotropic surrounding rock bending cracks under stress using methods such as energy release rate, weighted function, perturbation, and singular integral equations. These methods require the length of the bending portion to be much smaller than the length of the main crack. Furthermore, these methods combine analytical and numerical approaches, making it difficult to accurately determine the stress field of the bending crack. Summary of the Invention

[0004] Therefore, it is necessary to provide a stress field analysis method, apparatus, and computer equipment to address the aforementioned technical problems.

[0005] In a first aspect, this application provides a stress field analysis method, including:

[0006] Based on the orthogonal anisotropy parameters of the surrounding rock of the tunnel and the first geometric parameters of the cracks in the surrounding rock of the tunnel, the first coordinate representation of the cracks in the first plane is determined; wherein, the first plane is the plane containing the cracks in the plane where the surrounding rock of the tunnel is located, and the stress anisotropy of the cracks in the first plane is determined.

[0007] Based on the orthogonal anisotropy parameters and the first coordinate representation, the crack is mapped from the first plane to the second plane to obtain the second coordinate representation of the crack in the second plane; the stress on the crack in the second plane is isotropic.

[0008] Based on the second coordinate representation, the crack is transformed from the second plane to the unit circle to obtain the third coordinate representation of the crack on the unit circle;

[0009] Based on the third coordinate representation and the mapping relationship between the first plane and the second plane, the target stress and stress intensity factor of the crack on the first plane are determined.

[0010] Secondly, this application also provides a stress field analysis apparatus, comprising:

[0011] A plane construction module is used to determine the first coordinate representation of the crack in a first plane based on the orthogonal anisotropy parameters of the tunnel surrounding rock and the first geometric parameters of the crack in the tunnel surrounding rock; wherein, the first plane is a plane containing the crack in the plane where the tunnel surrounding rock is located, and the stress anisotropy of the crack in the first plane is also defined.

[0012] The first conversion module is used to map the crack from the first plane to the second plane according to the orthogonal anisotropy parameters and the first coordinate representation, so as to obtain the second coordinate representation of the crack in the second plane; the stress on the crack in the second plane is isotropic.

[0013] The second conversion module is used to convert the crack from the second plane to the unit circle according to the second coordinate representation, so as to obtain the third coordinate representation of the crack on the unit circle;

[0014] The stress analysis module is used to determine the target stress and stress intensity factor of the crack on the first plane based on the third coordinate representation and the mapping relationship between the first plane and the second plane.

[0015] Thirdly, this application also provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to perform the following steps:

[0016] Based on the orthogonal anisotropy parameters of the surrounding rock of the tunnel and the first geometric parameters of the cracks in the surrounding rock of the tunnel, the first coordinate representation of the cracks in the first plane is determined; wherein, the first plane is the plane containing the cracks in the plane where the surrounding rock of the tunnel is located, and the stress anisotropy of the cracks in the first plane is determined.

[0017] Based on the orthogonal anisotropy parameters and the first coordinate representation, the crack is mapped from the first plane to the second plane to obtain the second coordinate representation of the crack in the second plane; the stress on the crack in the second plane is isotropic.

[0018] Based on the second coordinate representation, the crack is transformed from the second plane to the unit circle to obtain the third coordinate representation of the crack on the unit circle;

[0019] Based on the third coordinate representation and the mapping relationship between the first plane and the second plane, the target stress and stress intensity factor of the crack on the first plane are determined.

[0020] Fourthly, this application also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, performs the following steps:

[0021] Based on the orthogonal anisotropy parameters of the surrounding rock of the tunnel and the first geometric parameters of the cracks in the surrounding rock of the tunnel, the first coordinate representation of the cracks in the first plane is determined; wherein, the first plane is the plane containing the cracks in the plane where the surrounding rock of the tunnel is located, and the stress anisotropy of the cracks in the first plane is determined.

[0022] Based on the orthogonal anisotropy parameters and the first coordinate representation, the crack is mapped from the first plane to the second plane to obtain the second coordinate representation of the crack in the second plane; the stress on the crack in the second plane is isotropic.

[0023] Based on the second coordinate representation, the crack is transformed from the second plane to the unit circle to obtain the third coordinate representation of the crack on the unit circle;

[0024] Based on the third coordinate representation and the mapping relationship between the first plane and the second plane, the target stress and stress intensity factor of the crack on the first plane are determined.

[0025] Fifthly, this application also provides a computer program product, including a computer program that, when executed by a processor, performs the following steps:

[0026] Based on the orthogonal anisotropy parameters of the surrounding rock of the tunnel and the first geometric parameters of the cracks in the surrounding rock of the tunnel, the first coordinate representation of the cracks in the first plane is determined; wherein, the first plane is the plane containing the cracks in the plane where the surrounding rock of the tunnel is located, and the stress anisotropy of the cracks in the first plane is determined.

[0027] Based on the orthogonal anisotropy parameters and the first coordinate representation, the crack is mapped from the first plane to the second plane to obtain the second coordinate representation of the crack in the second plane; the stress on the crack in the second plane is isotropic.

[0028] Based on the second coordinate representation, the crack is transformed from the second plane to the unit circle to obtain the third coordinate representation of the crack on the unit circle;

[0029] Based on the third coordinate representation and the mapping relationship between the first plane and the second plane, the target stress and stress intensity factor of the crack on the first plane are determined.

[0030] The aforementioned stress field analysis method, apparatus, and computer equipment determine the first coordinate representation of the crack in a first plane based on the orthogonal anisotropic parameters of the tunnel surrounding rock and the first geometric parameters of the crack in the tunnel surrounding rock. The first plane is the plane containing the crack within the tunnel surrounding rock, and the stress on the crack in the first plane is anisotropic. Based on the orthogonal anisotropic parameters and the first coordinate representation, the crack is mapped from the first plane to a second plane, obtaining the second coordinate representation of the crack in the second plane. Since the stress on the crack in the second plane is isotropic, the stress on the crack can be conveniently and accurately analyzed using the second plane. Furthermore, based on the second coordinate representation, the crack is transformed from the second plane to a unit circle, obtaining the third coordinate representation of the crack on the unit circle. Based on the third coordinate representation and the mapping relationship between the first and second planes, the target stress and stress intensity factor of the crack in the first plane are determined, enabling rapid and accurate analysis of the target stress and stress intensity factor. Attached Figure Description

[0031] To more clearly illustrate the technical solutions in the embodiments or related technologies of this application, the accompanying drawings used in the description of the embodiments or related technologies will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0032] Figure 1A This is a flowchart illustrating a stress field analysis method in one embodiment;

[0033] Figure 1B This is a schematic diagram of a quasi-orthogonal anisotropic planar element model constructed in one embodiment;

[0034] Figure 2A This is a schematic diagram of the process for determining the second coordinate representation of a crack in a second plane in one embodiment;

[0035] Figure 2B This is a schematic diagram of a crack being mapped from a first plane to a second plane in one embodiment;

[0036] Figure 3A This is a flowchart illustrating the process of determining the third coordinate representation of the crack on the unit circle in one embodiment;

[0037] Figure 3B This is a schematic diagram illustrating the mapping of the second plane of the crack onto a unit circle in one embodiment;

[0038] Figure 4 This is a flowchart illustrating the process of determining the target stress and stress intensity factor in one embodiment;

[0039] Figure 5This is a flowchart illustrating the process of determining the restoring potential of the stress field of the tunnel surrounding rock in the second plane in one embodiment.

[0040] Figure 6 This is a flowchart illustrating the process of determining the stress intensity factor of a crack in a first plane in one embodiment.

[0041] Figure 7A This is a flowchart illustrating the process of determining the stress intensity factor function of a crack in a first plane in one embodiment.

[0042] Figure 7B This is a schematic diagram illustrating the construction of a first tip coordinate system and a first polar coordinate system in a second plane in one embodiment;

[0043] Figure 7C This is a schematic diagram illustrating the construction of a first tip coordinate system and a first polar coordinate system on a first plane in one embodiment;

[0044] Figure 8A This is a schematic diagram of stress component analysis of cracks in different elastic materials in one embodiment;

[0045] Figure 8B This is a schematic diagram illustrating the stress intensity factor analysis of cracks in different elastic materials in one embodiment;

[0046] Figure 9 This is a structural block diagram of a stress field analysis device in one embodiment;

[0047] Figure 10 This is an internal structural diagram of a computer device in one embodiment. Detailed Implementation

[0048] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0049] The stress field analysis method provided in this application can be applied to stress analysis of cracks in the surrounding rock of tunnels. The stress field analysis method provided in this application can be executed by a computer device, which can be a server or a terminal with powerful computing capabilities.

[0050] In one exemplary embodiment, such as Figure 1A As shown, a stress field analysis method is provided. Taking the application of this method to a server as an example, the specific steps include:

[0051] S101, based on the orthogonal anisotropy parameters of the tunnel surrounding rock and the first geometric parameters of the cracks in the tunnel surrounding rock, determine the first coordinate representation of the cracks in the first plane.

[0052] Orthogonal anisotropy refers to a material exhibiting different mechanical properties (such as elastic modulus, Poisson's ratio, and strength) along three mutually perpendicular principal axes, with these physical properties distributed symmetrically along these axes. Orthogonal anisotropy parameters are physical quantities describing the differences in mechanical properties along these three principal axes, used to quantify the anisotropic characteristics of the material. In tunnel surrounding rock analysis, these parameters are core inputs for constructing mechanical models and predicting surrounding rock deformation and stability, directly affecting the accuracy of engineering design. Orthogonal anisotropy parameters include, but are not limited to, longitudinal elastic modulus, shear modulus, and Poisson's ratio.

[0053] The cracks in the surrounding rock of the tunnel are cracks generated within the tunnel's surrounding rock. In this embodiment, the crack is a folded crack, comprising a main crack and a folded crack. The first geometric parameter of the crack characterizes its shape and length, including but not limited to the length of the main crack, the length of the folded crack, and the folding angle. The first plane is the plane containing the crack within the plane of the tunnel's surrounding rock, and the stress on the crack in the first plane is anisotropic. In this embodiment, the first plane is the plane containing the quasi-orthogonal anisotropic planar element model of the cracked tunnel's surrounding rock. The first coordinates represent the coordinates of each point of the crack on the first plane.

[0054] Optionally, the orthogonal anisotropy parameters of the tunnel surrounding rock and the first geometric parameters of the cracks in the tunnel surrounding rock can be obtained through on-site measurements. Furthermore, a system such as... Figure 1B The quasi-orthogonal anisotropic planar element model shown is used as the first plane, and the first coordinate representation of the crack on the first plane is determined based on the first geometric parameters of the crack. The stress of the tunnel surrounding rock is σ. x , σ y , τ xy The coordinates of the first plane are constructed with the inflection point of the crack as the origin.

[0055] S102, based on the orthogonal anisotropy parameters and the first coordinate representation, the crack is mapped from the first plane to the second plane to obtain the second coordinate representation of the crack in the second plane.

[0056] The stress on the crack in the second plane is isotropic. The second coordinate represents the coordinates of each point on the crack in the second plane.

[0057] Optionally, to facilitate the analysis of the stress on the crack, it is necessary to map the crack from the first plane to the second plane. In the second plane, the stress in the tunnel surrounding rock is isotropic. Specifically, based on the material properties of the tunnel surrounding rock, an affine transformation function can be pre-constructed, and according to the affine transformation function, the crack can be mapped from the first plane to the second plane to obtain the second coordinate representation of the crack in the second plane.

[0058] S103, based on the second coordinate representation, the crack is transformed from the second plane to the unit circle to obtain the third coordinate representation of the crack on the unit circle.

[0059] The third coordinate represents the position of the crack on the unit circle.

[0060] It is understandable that, since the crack is a zigzag crack, meaning it includes two ends with a turning point, the different endpoints of the crack can be mapped to endpoints on the unit circle. A fractional linear transformation can be chosen to map the horizontal axis of the second plane onto the unit circle, and to map the endpoints of the crack onto points on the unit circle, thus obtaining a third coordinate representation of the crack on the unit circle.

[0061] In addition, the mapping function from the second plane to the unit circle can be determined by endpoint mapping.

[0062] S104. Based on the third coordinate representation and the mapping relationship between the first and second planes, determine the target stress and stress intensity factor of the crack on the first plane.

[0063] Wherein, the target stress is the stress of the stress field of the tunnel surrounding rock on the crack, including σ x , σ y , τ xy The stress intensity factor is used to quantify the stress field intensity at the crack tip of a cracked object when it is subjected to force, and its value directly determines whether the crack will propagate.

[0064] By combining complex variable functions and using the third coordinate representation, the restoring potential of the second plane can be determined, and then the stress on the crack in the second plane can be derived based on the restoring potential of the second plane. Furthermore, a mapping relationship between the first and second planes can be constructed based on the first and second coordinate representations.

[0065] Furthermore, based on the mapping relationship between the first plane and the second plane, the target stress on the crack in the first plane is derived according to the stress on the crack in the second plane.

[0066] Furthermore, based on the theory of elastic fracture mechanics, an expression for the stress field near the crack tip can be obtained. This expression includes the stress intensity factor. Further, by substituting the third coordinate representation into the expression for the stress field near the crack tip, an expression for the stress intensity factor at the crack tip in the second plane can be derived.

[0067] Furthermore, based on the stress field components near the crack tip in the first and second planes, the transformation relationship of the stress intensity factor function in the first and second planes is derived. Finally, based on the transformation relationship of the stress intensity factor function, the stress intensity factor of the crack in the first plane is derived from the expression of the stress intensity factor at the crack tip in the second plane.

[0068] In the aforementioned stress field analysis method, based on the orthogonal anisotropy parameters of the tunnel surrounding rock and the first geometric parameters of the cracks in the tunnel surrounding rock, the first coordinate representation of the crack in the first plane is determined. The first plane is the plane containing the crack within the tunnel surrounding rock, and the stress on the crack in the first plane is anisotropic. Based on the orthogonal anisotropy parameters and the first coordinate representation, the crack is mapped from the first plane to a second plane, obtaining the second coordinate representation of the crack in the second plane. Since the stress on the crack in the second plane is isotropic, the stress on the crack can be conveniently and accurately analyzed using the second plane. Furthermore, based on the second coordinate representation, the crack is transformed from the second plane to the unit circle, obtaining the third coordinate representation of the crack on the unit circle. Based on the third coordinate representation and the mapping relationship between the first and second planes, the target stress and stress intensity factor of the crack in the first plane are determined, enabling rapid and accurate analysis of the target stress and stress intensity factor.

[0069] Optionally, in one embodiment, such as Figure 2A As shown, a method for determining the second coordinate representation of a crack in a second plane is provided, specifically including the following steps:

[0070] S201, based on orthogonal anisotropy parameters, determine the characteristic root coefficients of the tunnel surrounding rock when the stress on the crack is isotropic.

[0071] Among them, the characteristic root coefficient of the tunnel surrounding rock is an important mechanical index used to evaluate the stability of the tunnel surrounding rock, reflecting the stress distribution and deformation characteristics of the surrounding rock after excavation.

[0072] Optionally, a mechanical model of the tunnel surrounding rock can be constructed, such as an elastic mechanical model, and orthogonal anisotropic parameters can be substituted into the constructed mechanical model. The mechanical model can then be differentiated to obtain the characteristic root coefficients of the tunnel surrounding rock when the stress on the crack is isotropic.

[0073] For example, the eigenvalue coefficients can be obtained by solving the following formula (1):

[0074] (1)

[0075] Among them, E x and E y These are the transverse and longitudinal elastic moduli, respectively; ν xy G is Poisson's ratio;xy Shear modulus; These are the different solutions for the characteristic root coefficients.

[0076] S202, based on the eigenvalue coefficients, construct the first mapping function between the first plane and the second plane.

[0077] Optionally, based on the eigenvalue coefficients, the first mapping function between the first and second planes can be expressed as the following formula (2):

[0078] (2)

[0079] in, These are the characteristic root coefficients; and These are the x-coordinate and y-coordinate of the crack on the first plane, respectively; and These are the x-coordinate and y-coordinate of the crack on the second plane, respectively.

[0080] S203, based on the first mapping function and the first coordinate representation, the crack is mapped from the first plane to the second plane to obtain the second coordinate representation of the crack in the second plane.

[0081] Optionally, the first coordinate representation can be substituted into the first mapping function, for example, into the above formula (2), to obtain the second coordinate representation of the crack in the second plane.

[0082] For example, such as Figure 2B The diagram shows the mapping of a crack from the first plane to the second plane. Line segment AD represents the main crack, and line segment BC represents the kink crack. The coordinate system is... Let be the coordinate system of the first plane. Let be the coordinate system for the second plane. In the first plane, The length of the main crack in the first plane is denoted as . Let be the length of the crack bending in the first plane. The main crack in the first plane and The included angle of the axis; For the crack in the first plane bending crack and The included angle of the axis; Let be the bending angle of the crack in the first plane. In the second plane, The length of the main crack in the second plane is denoted as . Let be the length of the crack bending at the second plane. The main crack in the second plane and The included angle of the axis; For the crack in the second plane bending crack and The included angle of the axis; The angle at which the crack bends in the second plane.

[0083] In this embodiment, by introducing the characteristic root coefficient of the tunnel surrounding rock when the stress on the crack is isotropic, the accuracy of the constructed first mapping function is ensured, thereby ensuring that the stress on the crack is isotropic on the second plane obtained based on the first mapping function.

[0084] In one exemplary embodiment, such as Figure 3A As shown, a method for determining the third coordinate representation of a crack on a unit circle is provided, which specifically includes the following steps:

[0085] S301, based on the second coordinate representation, determine the second geometric parameters of the crack in the second plane.

[0086] Among them, the second geometric parameter of the crack in the second plane characterizes the geometric parameters such as the shape and length of the crack in the second plane.

[0087] Optionally, based on the second coordinate representation of the crack in the second plane, and using the coordinates of each point, the length of the main crack, the length of the bending crack, and the bending angle in the second plane can be calculated. Simultaneously, the angle between the horizontal axis and the main crack, and the bending angle, can also be calculated in the coordinate system of the second plane.

[0088] S302, based on the second geometric parameters, construct a second mapping function between the second plane and the plane containing the unit circle.

[0089] Optionally, based on the second geometric parameters, the second mapping function between the second plane and the plane containing the unit circle can be expressed as:

[0090] (3)

[0091] (4)

[0092] (5)

[0093] in, , , These are related to the main crack length, the bending crack length, and the bending angle, respectively. The crack tips A and B, as well as the kink points C and D, are successively mapped onto the unit circle. , , , . The main crack in the plane (second plane) and The included angle of the axis is The bent part and The included angle of the axis is The bending angle is .

[0094] S303, according to the second mapping function, the second coordinate representation is converted into the third coordinate representation of the crack on the unit circle.

[0095] Optionally, the second coordinate representation can be converted into the third coordinate representation of the crack on the unit circle based on the second mapping function, i.e., the above formulas (3)-(5).

[0096] For example, such as Figure 3B The diagram shown illustrates the mapping of the second plane of the crack onto the unit circle. Wherein, Let A be the point on the unit circle mapped from the crack endpoint A. Let the point on the unit circle be the point mapped from the crack endpoint B. Let C be the point on the unit circle mapped from the crack endpoint C. Let D be the point on the unit circle mapped from the crack endpoint.

[0097] In this embodiment, by introducing a second mapping function, the accuracy of converting the second coordinate representation into the third coordinate representation of the crack on the unit circle is ensured.

[0098] Optionally, in one embodiment, such as Figure 4 As shown, a method for determining target stress and stress intensity factor is provided, specifically including the following steps:

[0099] S401, based on the third coordinate representation, determine the restoring potential of the stress field of the tunnel surrounding rock in the second plane.

[0100] Optionally, after mapping the cracks in the second plane onto the unit circle, the stress field of the tunnel surrounding rock is restored to its normal potential in the second plane. and It can be represented as:

[0101] (6)

[0102] The stress field of the tunnel surrounding rock is only subject to in-situ stress ( , and The function of the resetting potential is generally expressed in the form of:

[0103] (7)

[0104] (8)

[0105] in, and It is related to far-field stress.

[0106] S402, based on the reset potential, determine the reference stress on the crack in the second plane.

[0107] Optionally, the stress expression in the second plane is:

[0108] (9)

[0109] We obtain point z1=ω using the chain rule. T1r Stress field at (ζ1):

[0110] (10)

[0111] S403, based on the mapping relationship between the first plane and the second plane, and the reference stress on the crack in the second plane, determine the target stress on the crack in the first plane.

[0112] Optionally, by combining the mapping relationship between the first plane and the second plane, the stress relationship between the first plane and the second plane can be obtained:

[0113] (11)

[0114] Where, σ x , σ y, τ xy Let σ represent the stress at any point in the first plane. x1 , σ y1 , τ x1y1 This represents the stress at any point in the second plane.

[0115] Therefore, by substituting the reference stress on the crack in the second plane into the above formula, the target stress on the crack in the first plane can be obtained.

[0116] S404, based on the reset potential and the mapping relationship between the first plane and the second plane, determine the stress intensity factor of the crack in the first plane.

[0117] Optionally, a stress intensity factor calculation model can be pre-built, and the reset potential and the mapping relationship between the first plane and the second plane can be input into the stress intensity factor calculation model to obtain the stress intensity factor of the crack in the first plane.

[0118] In this embodiment, by introducing the restoring potential of the stress field of the tunnel surrounding rock in the second plane, and based on the mapping relationship between the first plane and the second plane, the accuracy and efficiency of the target stress and stress intensity factor of the determined crack in the first plane are ensured.

[0119] Optionally, in one embodiment, such as Figure 5As shown, a method for determining the restoring potential of the stress field of the surrounding rock of a tunnel in the second plane is provided, which specifically includes the following steps:

[0120] S501, obtain the boundary condition function of the complex potential function of the tunnel surrounding rock in the second plane.

[0121] Optionally, the complex potential function of the tunnel surrounding rock in the second plane and The boundary conditions are as follows:

[0122] (12)

[0123] S502, the boundary condition function is integrated to obtain the complex potential function of the tunnel surrounding rock in the second plane.

[0124] Optionally, Cauchy integration can be performed on the boundary condition function to obtain:

[0125] (13)

[0126] (14)

[0127] The simplified expression for the complex potential function is as follows:

[0128] (15)

[0129] (16)

[0130] (17)

[0131] Among them, P n It is a complex parameter, in It takes different values ​​when it is less than, equal to, or greater than 0; ω T1r (ζ1) is an expression containing N+3 terms when the Laurent series of the second mapping function is truncated.

[0132] S503 uses the third coordinate representation to update the complex potential function, obtaining the reset potential of the stress field of the tunnel surrounding rock in the second plane.

[0133] Optionally, the third coordinate representation can be substituted into the complex potential function to update the complex potential function and obtain the reset potential of the stress field of the tunnel surrounding rock in the second plane.

[0134] In this embodiment, by introducing a boundary condition function and performing integration on the boundary condition function, the accuracy of the complex potential function of the tunnel surrounding rock in the second plane is ensured. Furthermore, based on the third coordinate representation, the accuracy of the reset potential of the determined stress field of the tunnel surrounding rock in the second plane is ensured.

[0135] Optionally, in one embodiment, such as Figure 6 As shown, a method for determining the stress intensity factor of a crack in a first plane is provided, specifically including the following steps:

[0136] S601, based on the reset potential, construct the stress intensity factor function of the crack in the second plane.

[0137] Optionally, in the second plane, the stress intensity factor function of the crack is expressed as:

[0138] (18)

[0139] By rotating the coordinate system using rotational transformations in complex function theory, making the tangent at any crack tip parallel to the x-axis, and through simplified calculations, the stress intensity factor function of the crack in the second plane is expressed as follows:

[0140] (19)

[0141] (20)

[0142] in, and θ1 and θ2 are the coordinates of the crack tip A and B, respectively; δ1 is the angle between the main crack and the main axis x1, and θ1 is the angle between the bent part and the x1 axis.

[0143] S602, based on the mapping relationship between the first plane and the second plane, and the stress intensity factor function of the crack in the second plane, determine the stress intensity factor function of the crack in the first plane.

[0144] Optionally, based on the mapping relationship between the first plane and the second plane, the stress intensity factor function of the crack in the second plane can be mapped to the first plane, thus obtaining the stress intensity factor function of the crack in the first plane.

[0145] S603, determine the stress intensity factor of the crack in the first plane based on the stress intensity factor function of the crack in the first plane and the first geometric parameters of the crack.

[0146] Optionally, the stress intensity factor of the crack in the first plane can be obtained by updating the stress intensity factor function of the crack in the first plane based on the first geometric parameters of the crack.

[0147] In this embodiment, by introducing the stress intensity factor function of the crack in the second plane and combining it with the mapping relationship between the first plane and the second plane, the accuracy of the obtained stress intensity factor function of the crack in the first plane is ensured, thereby ensuring the accuracy of the obtained stress intensity factor of the crack in the first plane.

[0148] Optionally, in one embodiment, such as Figure 7A As shown, a method for determining the stress intensity factor function of a crack in the first plane is provided, specifically including the following steps:

[0149] S701, the stress field at the crack tip in the second plane is analyzed to obtain the stress components at the crack tip in the second plane.

[0150] To derive the relationship between the stress intensity factor functions of the first and second planes, it is necessary to obtain the stress components near the crack tip in both planes. Based on the second plane, a first tip coordinate system and a first polar coordinate system can be constructed with the crack tip as the origin. The stress components at the crack tip in the first tip coordinate system can be determined according to the second coordinate representation; where the horizontal axis of the first tip coordinate system represents the crack's extension direction. Based on the first tip coordinate system and the second geometric parameters, the stress components at the crack tip in the first tip coordinate system are converted into stress components at the crack tip in the second plane; where the second geometric parameters are determined according to the second coordinate representation.

[0151] Specifically, constructing such a plane Figure 7B The first tip coordinate system z shown 01 The first polar coordinate system (r1, θ1) has its origin at the crack tip A, and the crack surface is perpendicular to the x-axis. 01 The axes coincide. At z... 01 The stress components near the crack tip in the coordinate system can be expressed by the stress intensity factor as follows:

[0152] (twenty one)

[0153] (twenty two)

[0154] In the second plane, the stress components near the crack tip are expressed as:

[0155] (twenty three)

[0156] S702, the stress field at the crack tip in the first plane is analyzed to obtain the stress components at the crack tip in the first plane.

[0157] Similarly, based on the first plane, a second tip coordinate system and a second polar coordinate system are constructed with the crack tip as the origin, and the stress components of the crack tip in the second tip coordinate system are determined according to the first coordinate representation; wherein, the horizontal axis of the second tip coordinate system is the direction of crack extension; based on the second tip coordinate system and the first geometric parameters, the stress components of the crack tip in the second tip coordinate system are converted into the stress components of the crack tip in the first plane; wherein, the first geometric parameters are determined according to the first coordinate representation.

[0158] Specifically, constructing in the first plane as... Figure 7C The second tip coordinate system z0 and the second polar coordinate system (r, θ) are shown. In the plane of the second tip coordinate system, the stress component expression near the crack tip is:

[0159] (twenty four)

[0160] (25)

[0161] (26)

[0162] Where: θ is the angle between the x-axis and the x0-axis; s1 is the eigenvalue of coordinate system z1, which is related to the eigenvalue μ1 in the z-coordinate system. Based on the angular relationship between the z-plane and the z0-plane, the stress components near the crack tip in the z-plane can be expressed as:

[0163] (27)

[0164] S703, based on the mapping relationship between the first plane and the second plane, the stress component of the crack tip in the second plane, and the stress component of the crack tip in the first plane, determine the stress intensity factor transformation function between the first plane and the second plane.

[0165] (28)

[0166] S704. Determine the stress intensity factor function of the crack in the first plane based on the stress intensity factor function of the crack in the first plane and the stress intensity factor transformation function between the first plane and the second plane.

[0167] Optionally, based on the stress intensity factor transformation function between the first plane and the second plane, the stress intensity factor function of the crack in the first plane is substituted to obtain the stress intensity factor function of the crack in the first plane.

[0168] In this embodiment, by introducing the stress component of the crack tip in the second plane and the stress component of the crack tip in the first plane, the accuracy of the stress intensity factor transformation function between the determined first plane and the second plane is ensured, thereby ensuring the accuracy of the determined stress intensity factor function of the crack in the first plane.

[0169] In one embodiment, an application example is provided, where the crack in the surrounding rock of the tunnel is a bent crack with a main crack length a = 1 m and a bent portion length l, where (l / a = 0.5, 1, 2) and a bending angle α (α = -60°). The angle between the main crack and the x-axis is δ (δ = 0°). The far-field stress is... , , ( =1 MPa = =0), the orthotropic elastic constant is determined by the longitudinal elastic modulus E x and E y Shear modulus G xy And Poisson ratio ν xy Representation.

[0170] Step 1: Determine the characteristic root coefficients of the tunnel surrounding rock when the stress on the crack is isotropic, based on the orthogonal anisotropy parameters. Solving formula (1) in the above embodiment yields:

[0171] (29)

[0172] Step 2: Based on the eigenvalue coefficients, construct the first mapping function between the first and second planes. The constructed first mapping function is expressed as:

[0173] (30)

[0174] Simultaneously, a second mapping function is constructed between the second plane and the plane containing the unit circle:

[0175] (31)

[0176] (32)

[0177] (33)

[0178] (34)

[0179] The second mapping function of the crack in the second plane is expressed in Laurent series form as follows:

[0180] (35)

[0181] Where: P n These are complex parameters. The second mapping function... The derivative is expressed as follows:

[0182] (36)

[0183] Combining the above two formulas (35) and (36), we get:

[0184] (37)

[0185] Since the coefficients on both sides of the equation are the same, we obtain the following relationship:

[0186] (38)

[0187] Then P n It can be written as a recursive expression:

[0188] (39)

[0189] Since the Laurent series of the mapping function does not satisfy the condition at the crack tip A, the Laurent series of the mapping function needs to be truncated:

[0190] (40)

[0191] Because at the tip of the crack Three equations need to be satisfied, assuming the truncation mapping function contains N+3 terms:

[0192] (41)

[0193] Among them: T1, T2, and T3 are from the crack tip. The three equations that satisfy the condition uniquely determine the three additional coefficients.

[0194] Step 3: Determine the restoring potential of the stress field of the tunnel surrounding rock in the second plane. After mapping the cracks in the second plane onto the unit circle, the analytical expression of its restoring potential is denoted as: and :

[0195] (42)

[0196] The surrounding rock of the tunnel is only subjected to far-field stress ( , and The function of the resetting potential is generally expressed in the form of:

[0197] (43)

[0198] (44)

[0199] in accordance with and Boundary conditions satisfied:

[0200] (45)

[0201] Integrating both sides of the equation using Cauchy, we get:

[0202] (46)

[0203] (47)

[0204] The calculations and simplifications yield the expressions for the two reset potentials:

[0205] (48)

[0206] (49)

[0207] Substitute the crack parameters and boundary conditions into the reset potential expression to calculate its specific expression.

[0208] Step 4: Determine the target stress on the crack in the first plane. The stress expression in the second plane is:

[0209] (50)

[0210] We obtain point z1=ω using the chain rule. T1r Stress field at (ζ1):

[0211] (51)

[0212] Combining the first mapping function between the first plane and the second plane, the stress relationship between the first plane and the second plane can be obtained:

[0213] (52)

[0214] Where, σ x , σ y , τ xy σ represents the stress at any point in the z-plane. x1 , σ y1 , τ x1y1 This represents the stress at any point in the z1 plane.

[0215] Step 5: Determine the target stress and stress intensity factor of the crack in the first plane. In the second plane, the stress intensity factor function of the crack is:

[0216] (53)

[0217] By rotating the coordinate system using rotational transformations in complex function theory, making the tangent at any crack tip parallel to the x-axis, and through simplified calculations, the stress intensity factor at the crack tip in the second plane is expressed as follows:

[0218] (54)

[0219] (55)

[0220] in, and θ1 and θ2 are the coordinates of the crack tip A and B, respectively; δ1 is the angle between the main crack and the main axis x1, and θ1 is the angle between the bent part and the x1 axis.

[0221] To derive the relationship between the stress intensity factors of the first and second planes, it is necessary to obtain the stress components near the crack tip in both planes. A new coordinate system z is then constructed in the second plane. 01 The coordinate system is a polar coordinate system (r1, θ1), with its origin at the crack tip A, and the crack surface is perpendicular to the x-axis. 01 The axes coincide. In the z-axis... 01 The stress components near the crack tip in the coordinate system can be expressed by the stress intensity factor as follows:

[0222] (56)

[0223] (57)

[0224] In the second plane, the stress components near the crack tip are expressed as:

[0225] (58)

[0226] Similarly, a new coordinate system z0 and a polar coordinate system (r, θ) identical to the first plane can be constructed within the first plane. In the z0 plane, the expression for the stress components near the crack tip is:

[0227] (59)

[0228] (60)

[0229] (61)

[0230] Where: δ is the angle between the x-axis and the x0-axis; s1 is the characteristic root of the coordinate system of the second plane, which is related to the characteristic root μ1 in the coordinate system of the first plane.

[0231] Based on the angular relationship between the first and second planes, the stress components near the crack tip in the first plane can be expressed as:

[0232] (62)

[0233] By simplifying the above formula using the relationship between the stress components in the first and second planes, we obtain the stress intensity factor transformation function for the cracks in the first and second planes:

[0234] (63)

[0235] By substituting the specific parameters, the stress intensity factor in the first plane can be obtained.

[0236] like Figure 8A As shown, different l / a orthogonal anisotropy (E) is demonstrated. x / E y =0.25,1,8,32) and isotropic (E x / E y =1) The stress component σ of a bending crack along the positive y-axis in an elastic material. x The analytical solution and the finite element solution based on Abaqus are presented. The finite element solution is chosen to simulate a plate size of 200a * 200a. It can be seen that the stress component σ... x The stress decreases rapidly as y increases; the smaller y is, the faster the stress decreases, mainly due to stress concentration at the crack inflection point. When y increases (y / a > 2), the stress component σ of the bending crack... x Almost no effect; when E x / E y The larger the value, the greater the stress component σ. x The larger.

[0237] like Figure 8B As shown, the orthotropic anisotropy (E) is illustrated under different l / a values ​​(l / a = 0.5, 1, 2). x / E y =0.25) material and isotropy (E x / E y =1) The variations of Type I and Type II stress intensity factors at the tip B of the bending crack in the material with the bending angle. The variation trends of both analytical solutions and Abaqus-based finite element solutions were considered, with the plate size of the finite element solution being 200a*200a. The results show that as l / a increases, K... I Value and K IIThe values ​​all increase; with E x / E y The increase of K II The absolute value of decreases slightly; the analytical solution and the finite element solution are in good agreement.

[0238] It should be understood that although the steps in the flowcharts of the embodiments described above are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the embodiments described above may include multiple steps or multiple stages. These steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the steps or stages of other steps.

[0239] Based on the same inventive concept, this application also provides a stress field analysis apparatus for implementing the stress field analysis method described above. The solution provided by this apparatus is similar to the solution described in the above method; therefore, the specific limitations in one or more stress field analysis apparatus embodiments provided below can be found in the limitations of the stress field analysis method described above, and will not be repeated here.

[0240] In one exemplary embodiment, such as Figure 9 As shown, a stress field analysis device 900 is provided, including: a planar construction module 910, a first conversion module 920, a second conversion module 930, and a stress analysis module 940, wherein:

[0241] The plane construction module 910 is used to determine the first coordinate representation of the crack in the first plane based on the orthogonal anisotropy parameters of the tunnel surrounding rock and the first geometric parameters of the crack in the tunnel surrounding rock; wherein, the first plane is the plane containing the crack in the plane where the tunnel surrounding rock is located, and the stress anisotropy of the crack in the first plane.

[0242] The first conversion module 920 is used to map the crack from the first plane to the second plane according to the orthogonal anisotropy parameters and the first coordinate representation, so as to obtain the second coordinate representation of the crack in the second plane; the stress on the crack in the second plane is isotropic.

[0243] The second conversion module 930 is used to convert the crack from the second plane to the unit circle according to the second coordinate representation, so as to obtain the third coordinate representation of the crack on the unit circle.

[0244] The stress analysis module 940 is used to determine the target stress and stress intensity factor of the crack in the first plane based on the third coordinate representation and the mapping relationship between the first plane and the second plane.

[0245] In one embodiment, the first conversion module 920 is specifically used for:

[0246] Based on the orthogonal anisotropy parameters, the characteristic root coefficients of the tunnel surrounding rock are determined when the stress on the crack is isotropic; based on the characteristic root coefficients, a first mapping function is constructed between the first plane and the second plane; based on the first mapping function and the first coordinate representation, the crack is mapped from the first plane to the second plane to obtain the second coordinate representation of the crack in the second plane.

[0247] In one embodiment, the second conversion module 930 is specifically used for:

[0248] Based on the second coordinate representation, determine the second geometric parameters of the crack on the second plane; based on the second geometric parameters, construct a second mapping function between the second plane and the plane containing the unit circle; based on the second mapping function, convert the second coordinate representation into a third coordinate representation of the crack on the unit circle.

[0249] In one embodiment, the stress analysis module 940 includes:

[0250] The first determining unit is used to determine the restoring potential of the stress field of the tunnel surrounding rock in the second plane based on the third coordinate representation.

[0251] The second determining unit is used to determine the reference stress on the crack in the second plane based on the reset potential.

[0252] The third determining unit is used to determine the target stress of the crack in the first plane based on the mapping relationship between the first plane and the second plane, and the reference stress of the crack in the second plane.

[0253] The fourth determining unit is used to determine the stress intensity factor of the crack in the first plane based on the reset potential and the mapping relationship between the first plane and the second plane.

[0254] In one embodiment, the first determining unit is specifically used for:

[0255] Obtain the boundary condition function of the complex potential function of the tunnel surrounding rock in the second plane; integrate the boundary condition function to obtain the complex potential function of the tunnel surrounding rock in the second plane; use the third coordinate to represent and update the complex potential function to obtain the reset potential of the stress field of the tunnel surrounding rock in the second plane.

[0256] In one embodiment, the fourth determining unit includes:

[0257] Construct sub-elements to generate the stress intensity factor function of the crack in the second plane based on the reset potential.

[0258] The first determining sub-unit is used to determine the stress intensity factor function of the crack in the first plane based on the mapping relationship between the first plane and the second plane, and the stress intensity factor function of the crack in the second plane.

[0259] The second determining sub-unit is used to determine the stress intensity factor of the crack in the first plane based on the stress intensity factor function of the crack in the first plane and the first geometric parameters of the crack.

[0260] In one embodiment, the second determining subunit includes:

[0261] The first element is used to analyze the stress field at the crack tip in the second plane and obtain the stress components at the crack tip in the second plane.

[0262] The second sub-element is used to analyze the stress field at the crack tip in the first plane and obtain the stress components at the crack tip in the first plane.

[0263] The third slave unit is used to determine the stress intensity factor transformation function between the first plane and the second plane based on the mapping relationship between the first plane and the second plane, the stress component of the crack tip in the second plane, and the stress component of the crack tip in the first plane.

[0264] The fourth slave unit is used to determine the stress intensity factor function of the crack in the first plane based on the stress intensity factor function of the crack in the first plane and the stress intensity factor transformation function between the first plane and the second plane.

[0265] In one embodiment, the first slave unit is specifically used for:

[0266] Based on the second plane, a first tip coordinate system and a first polar coordinate system are constructed with the crack tip as the origin. The stress components of the crack tip in the first tip coordinate system are determined according to the second coordinate representation. The horizontal axis of the first tip coordinate system is the direction of crack extension. Based on the first tip coordinate system and the second geometric parameters, the stress components of the crack tip in the first tip coordinate system are converted into the stress components of the crack tip in the second plane. The second geometric parameters are determined according to the second coordinate representation.

[0267] The aforementioned stress field analysis device determines the first coordinate representation of the crack in a first plane based on the orthogonal anisotropic parameters of the tunnel surrounding rock and the first geometric parameters of the crack in the tunnel surrounding rock. The first plane is the plane containing the crack within the tunnel surrounding rock, and the stress on the crack in the first plane is anisotropic. Based on the orthogonal anisotropic parameters and the first coordinate representation, the crack is mapped from the first plane to a second plane, obtaining the second coordinate representation of the crack in the second plane. Since the stress on the crack in the second plane is isotropic, the stress on the crack can be conveniently and accurately analyzed using the second plane. Furthermore, based on the second coordinate representation, the crack is transformed from the second plane to a unit circle, obtaining the third coordinate representation of the crack on the unit circle. Based on the third coordinate representation and the mapping relationship between the first and second planes, the target stress and stress intensity factor of the crack in the first plane are determined, enabling rapid and accurate analysis of the target stress and stress intensity factor.

[0268] Each module in the aforementioned stress field analysis device can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in the processor of a computer device in hardware form or independent of it, or stored in the memory of a computer device in software form, so that the processor can call and execute the operations corresponding to each module.

[0269] In one exemplary embodiment, a computer device is provided, which may be a server, and its internal structure diagram may be as follows: Figure 10 As shown, this computer device includes a processor, memory, input / output (I / O) interfaces, and a communication interface. The processor, memory, and I / O interfaces are connected via a system bus, and the communication interface is also connected to the system bus via the I / O interfaces. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and databases. The internal memory provides the environment for the operating system and computer programs stored in the non-volatile storage media to run. The I / O interfaces are used for exchanging information between the processor and external devices. The communication interface is used for communicating with external terminals via a network connection. When the computer program is executed by the processor, it implements a stress field analysis method.

[0270] Those skilled in the art will understand that Figure 10 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0271] In one exemplary embodiment, a computer device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps involved in the stress field analysis method provided in the above embodiments.

[0272] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the steps involved in the stress field analysis method provided in the above embodiments.

[0273] In one embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps involved in the stress field analysis method provided in the above embodiments.

[0274] It should be noted that the data involved in this application (including but not limited to data used for analysis, data stored, data displayed, etc.) are all information and data that have been fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0275] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments described above. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM). The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0276] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0277] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A stress field analysis method, characterized in that, The method includes: Based on the orthogonal anisotropy parameters of the surrounding rock of the tunnel and the first geometric parameters of the cracks in the surrounding rock of the tunnel, the first coordinate representation of the cracks in the first plane is determined; wherein, the first plane is the plane containing the cracks in the plane where the surrounding rock of the tunnel is located, and the stress anisotropy of the cracks in the first plane is determined. Based on the orthogonal anisotropy parameters and the first coordinate representation, the crack is mapped from the first plane to the second plane to obtain the second coordinate representation of the crack in the second plane; the stress on the crack in the second plane is isotropic. Based on the second coordinate representation, the crack is transformed from the second plane to the unit circle to obtain the third coordinate representation of the crack on the unit circle; Based on the third coordinate representation and the mapping relationship between the first plane and the second plane, the target stress and stress intensity factor of the crack on the first plane are determined.

2. The method according to claim 1, characterized in that, The step of mapping the crack from the first plane to the second plane based on the orthogonal anisotropy parameters and the first coordinate representation to obtain the second coordinate representation of the crack in the second plane includes: Based on the orthogonal anisotropy parameters, determine the characteristic root coefficients of the tunnel surrounding rock when the stress on the crack is isotropic; Based on the eigenvalue coefficients, a first mapping function is constructed between the first plane and the second plane; Based on the first mapping function and the first coordinate representation, the crack is mapped from the first plane to the second plane to obtain the second coordinate representation of the crack in the second plane.

3. The method according to claim 1, characterized in that, The step of transforming the crack from the second plane to the unit circle based on the second coordinate representation to obtain the third coordinate representation of the crack on the unit circle includes: Based on the second coordinate representation, determine the second geometric parameters of the crack in the second plane; Based on the second geometric parameters, a second mapping function is constructed between the second plane and the plane containing the unit circle; According to the second mapping function, the second coordinate representation is converted into a third coordinate representation of the crack on the unit circle.

4. The method according to claim 1, characterized in that, The step of determining the target stress and stress intensity factor of the crack on the first plane based on the third coordinate representation and the mapping relationship between the first plane and the second plane includes: Based on the third coordinate representation, the restoring potential of the stress field of the tunnel surrounding rock in the second plane is determined; Based on the reset potential, determine the reference stress that the crack experiences in the second plane; Based on the mapping relationship between the first plane and the second plane, and the reference stress on the crack in the second plane, the target stress on the crack in the first plane is determined; Based on the reset potential and the mapping relationship between the first plane and the second plane, the stress intensity factor of the crack in the first plane is determined.

5. The method according to claim 4, characterized in that, Determining the restoring potential of the stress field of the tunnel surrounding rock in the second plane based on the third coordinate representation includes: Obtain the boundary condition function of the complex potential function of the tunnel surrounding rock in the second plane; Integrating the boundary condition function yields the complex potential function of the tunnel surrounding rock in the second plane; Using the third coordinate representation, the complex potential function is updated to obtain the reset potential of the stress field of the tunnel surrounding rock in the second plane.

6. The method according to claim 4, characterized in that, The step of determining the stress intensity factor of the crack in the first plane based on the reset potential and the mapping relationship between the first plane and the second plane includes: Based on the reset potential, construct the stress intensity factor function of the crack in the second plane; Based on the mapping relationship between the first plane and the second plane, and the stress intensity factor function of the crack in the second plane, the stress intensity factor function of the crack in the first plane is determined. The stress intensity factor of the crack in the first plane is determined based on the stress intensity factor function of the crack in the first plane and the first geometric parameter of the crack.

7. The method according to claim 6, characterized in that, The step of determining the stress intensity factor function of the crack in the first plane based on the mapping relationship between the first plane and the second plane, and the stress intensity factor function of the crack in the second plane, includes: The stress field at the crack tip in the second plane is analyzed to obtain the stress components at the crack tip in the second plane. The stress field at the crack tip in the first plane is analyzed to obtain the stress components at the crack tip in the first plane. Based on the mapping relationship between the first plane and the second plane, the stress component of the crack tip in the second plane, and the stress component of the crack tip in the first plane, the stress intensity factor transformation function between the first plane and the second plane is determined; The stress intensity factor function of the crack in the first plane is determined based on the stress intensity factor function of the crack in the first plane and the stress intensity factor transformation function between the first plane and the second plane.

8. The method according to claim 7, characterized in that, The analysis of the stress field at the crack tip in the second plane to obtain the stress components at the crack tip in the second plane includes: Based on the second plane, a first tip coordinate system and a first polar coordinate system are constructed with the crack tip as the origin, and the stress components of the crack tip in the first tip coordinate system are determined according to the second coordinate representation; wherein, the horizontal axis of the first tip coordinate system is the extension direction of the crack. Based on the first tip coordinate system and the second geometric parameters, the stress component of the crack tip in the first tip coordinate system is converted into the stress component of the crack tip in the second plane; wherein, the second geometric parameters are determined according to the second coordinate representation.

9. A stress field analysis device, characterized in that, The device includes: A plane construction module is used to determine the first coordinate representation of the crack in a first plane based on the orthogonal anisotropy parameters of the tunnel surrounding rock and the first geometric parameters of the crack in the tunnel surrounding rock; wherein, the first plane is a plane containing the crack in the plane where the tunnel surrounding rock is located, and the stress anisotropy of the crack in the first plane is also defined. The first conversion module is used to map the crack from the first plane to the second plane according to the orthogonal anisotropy parameters and the first coordinate representation, so as to obtain the second coordinate representation of the crack in the second plane; the stress on the crack in the second plane is isotropic. The second conversion module is used to convert the crack from the second plane to the unit circle according to the second coordinate representation, so as to obtain the third coordinate representation of the crack on the unit circle; The stress analysis module is used to determine the target stress and stress intensity factor of the crack on the first plane based on the third coordinate representation and the mapping relationship between the first plane and the second plane.

10. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 6.

Images